In the LUCHI patents of 1967/68 (Italy no. 818,060, West Germany no. 1,815,936, U.S. Pat. No. 3,650,126) and in the subsequent HOFFMAN patents of 1977/78 (Italy no. 1,078,922, West Germany no. 2825864.2, U.S. Pat. No. 4,188,804), a method has been described for the formation of a pocket in a tubular manufactured article (such as a heel for a woman's stocking or man's sock or in general, and/or the toe of such a manufactured article or other). Production is by means of at least two yarn feeds, with reciprocating motion of the needle cylinder, with such an arrangement that a group of rows of stitches according to a given sequence of yarns is followed by a group of rows of stitches according to a reversed sequence of these yarns. Each feed supplies the yarn to needles of an arc which is staggered in relation to the arc which has been supplied with yarn from another feed. The arcs are superposed partially in an intermediate zone of greater development of the pocket. The rows of stitches formed during the formation of the pocket are comprised in the arc of needles defined by the two rows of stitches which are most staggered in relation to one another. A number of arcs of needles are all partially staggered in relation to one another in the same direction and are obtained with yarns fed from the same number of staggered feeds. Moreover, the angular development of the pocket is varied by variation of the stitches at the external ends of the rows of stitches which are most staggered in relation to one another.